Question: Simplify the following expression: $ q = \dfrac{-4}{9} - \dfrac{9}{x + 6} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{x + 6}{x + 6}$ $ \dfrac{-4}{9} \times \dfrac{x + 6}{x + 6} = \dfrac{-4x - 24}{9x + 54} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{9}{x + 6} \times \dfrac{9}{9} = \dfrac{81}{9x + 54} $ Therefore $ q = \dfrac{-4x - 24}{9x + 54} - \dfrac{81}{9x + 54} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-4x - 24 - 81 }{9x + 54} $ Distribute the negative sign: $q = \dfrac{-4x - 24 - 81}{9x + 54}$ $q = \dfrac{-4x - 105}{9x + 54}$